We report the integral cross sections per scatterer (i.e. elastic collision, phonon excitations, vibrational excitations, electronic excitations and ionization) for 1-100 eV electron scattering in an amorphous film of ice condensed at a temperature of 14 K. The integral cross sections are determined relative to the total from a two-stream multiple-scattering analysis of the electron energy distribution backscattered from the film. Their energy dependence is obtained from both the analysis of the elastic electron reflectivity as a function of the film thickness and the vibrational electron energy-loss spectra measured for several incident energies and large film thickness. The magnitude and various features found in the energy dependence of the cross sections are discussed, whenever possible, by comparison with data and with scattering mechanisms available in the gas phase. Microcospic effects, which are implicitly included in cross sections determined in this way, are discussed in terms of interference and coherent multiple-scattering contributions among the scattering sites as well as interactions of the scattering sites with their neighbors in the condensed phase.